2020/05/31 by Abouzeid M. Shalaby · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1140/epjc/s10052-021-08884-5
In this version, we used arbitrary parameter which has been optmized and the corresponding errors are estimated
arxiv created 2020/08/24 · arxiv updated 2021/02/24
We extract the ε-expansion from the recently obtained seven-loop g-expansion for the renormalization group functions of the O(N)-symmetric model. The different series obtained for the critical exponents ν, ω and η have been resummed using our recently introduced hypergeometric-Meijer resummation algorithm. In three dimensions, very precise results have been obtained for all the critical exponents for N=0,1,2,3 and 4. To shed light on the obvious improvement of the predictions at this order, we obtained the divergence of the specific heat critical exponent α for the XY model. We found the result -0.0123(11) which is compatible with the famous experimental result of -0.0127(3) from the specific heat of zero gravity liquid helium superfluid transition while the six-loop Borel with conformal mapping resummation result in literature gives the value -0.007(3). For the challenging case of resummation of the ε-expansion series in two dimensions, we showed that our resummation results reflect a significant improvement to the previous six-loop resummation predictions.